Guidelines for Controlling Pore Radii From Nonlinear Analysis of a Two-Dimensional Model of Electroporation

Electroporation, in which strong electric pulses create transient pores in the cell membrane, is commonly used as a method for delivering molecules into cells. One of the pulsing protocols used in practice, a two-pulse protocol, creates a certain number of pores (Num) with a short, large electric pulse, and then controls the pore size with a second, smaller electric pulse of strength V0 . This study uses nonlinear analysis of an electroporation model to determine guidelines for the magnitude of V0 and Num that will produce pores of a desired radius (r). Analysis reveals that for Num between 85 and 3190, number and type of fixed points (FPs) depend on Num and V0 . For this range of Num, there exist two stable FPs and one unstable FP, and increasing V0 beyond a certain threshold (V0 th ) drives the system to the FP with larger r. V0 th can be fit to a function that is linearly dependent on Num. This study shows that for a given Num created by the first pulse, choice of V0 will allow the experimenter to optimize pore size for a specific application.Copyright © 2007 by ASME